Grouped Latin Hypercube Designs with Controlled Correlations

Latin hypercube designs are widely used for running computer experiments. Motivated by modern computer experiments with grouped inputs, we propose a new type of Latin hypercube design, called grouped Latin hypercube design with controlled correlations (GLHD-CC). This special Latin hypercube partitions all columns into disjoint groups where controlled column-wise correlations across all inputs is achieved and inputs within the same group have lower column-wise correlations than those from different groups. Our construction method for this new design uses a multivariate block orthogonalization technique in multivariate linear regression to simultaneously control correlations across multiple variables. We present an efficient algorithm for enabling the construction method and establish its theoretical properties. The algorithm is flexible in run size and input dimension, with effectiveness demonstrated through three popular test functions and a case study on a true black-box simulator.